The 1960s called; They want their unfounded assumption back.The reality is that most people do want children, and they'll have as many as they can afford.
The reality is that most people want sex, and they'll have as many children as they want, plus a random number implied by the quality of contraception available.
When the quality of available contraception becomes sufficiently high, we observe that women, on average, choose to have fewer than two children, regardless of their level of wealth. So while most people probably do want children, the average size of that want, globally, is somewhat less than two.
There are, of course, plenty of individual exceptions, and plenty of local exceptions too, due to random variations in personal preference, and/or the use of large families as symbols of religious belief, wealth, or social status, for example.
Where having children is particularly expensive and family size is easily managed, you would expect to see some people having larger families as a way of advertising their wealth. Your membership of such a sub-set of humanity is not, however, evidence of its universality; And the global birth rate numbers demonstrate that it's not, currently, a global circumstance.
My 'membership' is a part of the exact wealthy nations that we're discussing, so I think it's fair to extrapolate that experience to the scope of this discussion. I doubt that people have more children to flaunt wealth, they have more children because they want more children and can afford them. But you don't often see anyone go beyond four unless they live on a farm, because of space constraints.
You'll get no argument from me on contraception, but cost of living is most definitely a massive (massive) factor for my generation. For us, it's not just a matter of having grit and toughing it out, it, it's a matter of not starving or ending up homeless in old age.
We're working in precarious jobs, with poor salaries, can barely afford housing, pensions no longer exist, most of our parents can barely help, we have student debt. Kids? lol. It's not just a matter of us having the preference of 2, it's a matter of many of us only being able to afford 1, or 0. Mostly 0.